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    \section{Ice Sheets and Climate - Eric Keenan - Homework \#
2}\label{ice-sheets-and-climate---eric-keenan---homework-2}

    \begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}1}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np}
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{\color{incolor}In [{\color{incolor}2}]:} \PY{c+c1}{\PYZsh{} Function to load in aws data}
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            \PY{n}{time\PYZus{}series} \PY{o}{=} \PY{n}{time\PYZus{}series}\PY{o}{.}\PY{n}{replace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mf}{999.50000}\PY{p}{,} \PY{n}{np}\PY{o}{.}\PY{n}{nan}\PY{p}{)}
            
            \PY{c+c1}{\PYZsh{} Trim to year}
            \PY{n}{time\PYZus{}series} \PY{o}{=} \PY{n}{time\PYZus{}series}\PY{o}{.}\PY{n}{truncate}\PY{p}{(}\PY{n}{before}\PY{o}{=}\PY{n}{pd}\PY{o}{.}\PY{n}{to\PYZus{}datetime}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{1998\PYZhy{}01\PYZhy{}01 00:00:00}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,} \PYZbs{}
                                               \PY{n}{after}\PY{o}{=}\PY{n}{pd}\PY{o}{.}\PY{n}{to\PYZus{}datetime}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{1998\PYZhy{}12\PYZhy{}31 00:00:00}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{)}
        
            \PY{k}{return} \PY{n}{time\PYZus{}series}
\end{Verbatim}


    \section{Problem 1}\label{problem-1}

\paragraph{1.a. The temperature and wind sensors height above the snow
surface changes with time as the station becomes burried. Thus to
provide a consistent record the observations are corrected to 2 m and 10
m above the
surface.}\label{a.-the-temperature-and-wind-sensors-height-above-the-snow-surface-changes-with-time-as-the-station-becomes-burried.-thus-to-provide-a-consistent-record-the-observations-are-corrected-to-2-m-and-10-m-above-the-surface.}

\paragraph{1.b. For this assignment we will look at year
1998.}\label{b.-for-this-assignment-we-will-look-at-year-1998.}

    \section{Problem 2 - AWS 4}\label{problem-2---aws-4}

\paragraph{2.a. 2 m air temperature is generally higher in the summer
and with larger variability in the winter than summer. At AWS 4 there is
no readily apparent seasonal cycle in wind speed. However there is large
variability in daily averaged wind speeds. Notably two periods of low
wind speed in winter coincide with large surface inversions, likely due
to a lack of turbulence caused by low wind
speed.}\label{a.-2-m-air-temperature-is-generally-higher-in-the-summer-and-with-larger-variability-in-the-winter-than-summer.-at-aws-4-there-is-no-readily-apparent-seasonal-cycle-in-wind-speed.-however-there-is-large-variability-in-daily-averaged-wind-speeds.-notably-two-periods-of-low-wind-speed-in-winter-coincide-with-large-surface-inversions-likely-due-to-a-lack-of-turbulence-caused-by-low-wind-speed.}

\paragraph{2.b. Difference between surface temperature and 2 m air
temperature are largest on cold winter days with low wind speed. This is
important for the sensible heat flux which is driven by a near surface
temperature gradient! See scatter plots below. The difference is
smallest on windy
days.}\label{b.-difference-between-surface-temperature-and-2-m-air-temperature-are-largest-on-cold-winter-days-with-low-wind-speed.-this-is-important-for-the-sensible-heat-flux-which-is-driven-by-a-near-surface-temperature-gradient-see-scatter-plots-below.-the-difference-is-smallest-on-windy-days.}

    \begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}3}]:} \PY{c+c1}{\PYZsh{} File paths}
        \PY{n}{aws4\PYZus{}path} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS4\PYZus{}DAY.txt}\PY{l+s+s2}{\PYZdq{}}
        \PY{n}{aws9\PYZus{}path} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS9\PYZus{}DAY.txt}\PY{l+s+s2}{\PYZdq{}}
        
        \PY{c+c1}{\PYZsh{} Load data (colum numbers: 4 = t2m, 8 = 10 m wind, 5 = surface temperature)}
        \PY{n}{aws4\PYZus{}t2m} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{4}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mf}{273.15}
        \PY{n}{aws4\PYZus{}ws10m} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{8}\PY{p}{)}
        \PY{n}{aws4\PYZus{}ts} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{5}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mf}{273.15}
        \PY{c+c1}{\PYZsh{} aws4\PYZus{}ts = aws\PYZus{}timeseries(aws4\PYZus{}path, 6) \PYZhy{} 273.15}
        \PY{n}{aws4\PYZus{}SHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{15}\PY{p}{)}
        \PY{n}{aws4\PYZus{}LHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{16}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Calculations}
        \PY{n}{aws4\PYZus{}tdiff} \PY{o}{=} \PY{n}{aws4\PYZus{}ts} \PY{o}{\PYZhy{}} \PY{n}{aws4\PYZus{}t2m}
        
        \PY{c+c1}{\PYZsh{} Plot 2 meter temperature }
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}t2m}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2 m Temperature}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Degrees C}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot 10 meter wind speed }
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ws10m}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{10 m Wind Speed}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{m/s}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot surface temperature minus 2 meter temperature}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}tdiff}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Temperature minus 2 m Temperature}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Degrees C}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot wind speed vs temperature difference }
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{5}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{aws4\PYZus{}ws10m}\PY{p}{,} \PY{n}{aws4\PYZus{}tdiff}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{10 m Wind Speed [m/s]}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Temperature minus 2 m Temperature [C]}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot sensible heat flux vs temperature difference}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{5}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{aws4\PYZus{}SHF}\PY{p}{,} \PY{n}{aws4\PYZus{}tdiff}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Sensible Heat Flux [W/m\PYZca{}2]}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Temperature minus 2 m Temperature [C]}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
\end{Verbatim}


    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_0.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_1.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_2.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_3.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_4.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \section{Problem 3 - Calculate Surface Temperature at AWS
4}\label{problem-3---calculate-surface-temperature-at-aws-4}

    \begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}4}]:} \PY{c+c1}{\PYZsh{} Calculate surface temperature 14}
        \PY{n}{aws4\PYZus{}OLWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{14}\PY{p}{)} 
        \PY{n}{aws4\PYZus{}ts\PYZus{}calc} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{power}\PY{p}{(}\PY{n}{aws4\PYZus{}OLWR} \PY{o}{/} \PY{p}{(}\PY{l+m+mf}{0.97} \PY{o}{*} \PY{l+m+mf}{5.67e\PYZhy{}8}\PY{p}{)}\PY{p}{,} \PY{l+m+mf}{0.25}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mf}{273.15}
        
        \PY{c+c1}{\PYZsh{} Plot}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ts\PYZus{}calc}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{My Calculation}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ts}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Data Set Calculation}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Temperature}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Degrees C}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}4}]:} <matplotlib.legend.Legend at 0x1278b22e8>
\end{Verbatim}
            
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_7_1.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \section{Problem 4 - Radiative and Turbulent
Fluxes}\label{problem-4---radiative-and-turbulent-fluxes}

\paragraph{4.a. Seasonal Cycles: Radiative fluxes have a strong seasonal
cycle, higher in the summer, lower in the winter due to the rising sun
and warming of the atmosphere and snow surface. The sensible heat flux
is also higher in winter. The ground heat flux appears to have no
signficant seasonal cycle. Latent heat flux is either very small or zero
in winter (no phasse changes) but then negative in summer. This can
likely be explained by refreezing of surface meltwater or
deposition.}\label{a.-seasonal-cycles-radiative-fluxes-have-a-strong-seasonal-cycle-higher-in-the-summer-lower-in-the-winter-due-to-the-rising-sun-and-warming-of-the-atmosphere-and-snow-surface.-the-sensible-heat-flux-is-also-higher-in-winter.-the-ground-heat-flux-appears-to-have-no-signficant-seasonal-cycle.-latent-heat-flux-is-either-very-small-or-zero-in-winter-no-phasse-changes-but-then-negative-in-summer.-this-can-likely-be-explained-by-refreezing-of-surface-meltwater-or-deposition.}

\paragraph{4.b. Similarities and Differences: Both sites have a strong
seasonal cycle in shortwave radiation because of their high latitude,
however AWS 9 has significantly higher incoming SWR because of higher
elevation, despite a more southerly latitude. AWS 4 has higher longwave
fluxes because of a warmer climate regime. In summer AWS 4 has a larger
SHF because of a warmer atmosphere, however, the SHF can be positive in
winter as both sites, indicating the atmosphere can be warmer than the
surface (surface inversion) at both locations. The LHF is larger in
magnitude at AWS 4 because of either larger meltwater refreezing or
deposition.}\label{b.-similarities-and-differences-both-sites-have-a-strong-seasonal-cycle-in-shortwave-radiation-because-of-their-high-latitude-however-aws-9-has-significantly-higher-incoming-swr-because-of-higher-elevation-despite-a-more-southerly-latitude.-aws-4-has-higher-longwave-fluxes-because-of-a-warmer-climate-regime.-in-summer-aws-4-has-a-larger-shf-because-of-a-warmer-atmosphere-however-the-shf-can-be-positive-in-winter-as-both-sites-indicating-the-atmosphere-can-be-warmer-than-the-surface-surface-inversion-at-both-locations.-the-lhf-is-larger-in-magnitude-at-aws-4-because-of-either-larger-meltwater-refreezing-or-deposition.}

    \begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}5}]:} \PY{c+c1}{\PYZsh{} Load data and perform 10 day running means}
        \PY{n}{aws4\PYZus{}ISWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{11}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)}
        \PY{n}{aws4\PYZus{}OSWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{12}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)}
        \PY{n}{aws4\PYZus{}ILWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{13}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)}
        \PY{n}{aws4\PYZus{}OLWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{14}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws4\PYZus{}SHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{15}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws4\PYZus{}LHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{16}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws4\PYZus{}GHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{17}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        
        \PY{n}{aws9\PYZus{}ISWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{11}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}OSWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{12}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}ILWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{13}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}OLWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{14}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}SHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{15}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}LHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{16}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}GHF} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{17}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        
        \PY{c+c1}{\PYZsh{} Plot AWS 4}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ISWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{ISWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}OSWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{OSWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ILWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{ILWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}OLWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{c}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{OLWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}SHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{g}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{SHF}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}LHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{LHF}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot AWS 9}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}ISWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}OSWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}ILWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}OLWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{c\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}SHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{g\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}LHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Radiative and Turbulent Fluxes \PYZhy{} AWS 4 Solid \PYZhy{} AWS 9 \PYZhy{} Dashed}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{W/m\PYZca{}2}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot AWS 9 zoom on on turbylent fluxes}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ISWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{ISWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}OSWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{OSWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ILWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{ILWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}OLWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{c}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{OLWR}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}SHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{g}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{SHF}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}LHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{LHF}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot AWS 9}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}ISWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}OSWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}ILWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}OLWR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{c\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}SHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{g\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}LHF}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylim}\PY{p}{(}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{40}\PY{p}{,} \PY{l+m+mi}{40}\PY{p}{]}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Radiative and Turbulent Fluxes \PYZhy{} AWS 4 Solid \PYZhy{} AWS 9 \PYZhy{} Dashed}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{W/m\PYZca{}2}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}5}]:} Text(0, 0.5, 'W/m\^{}2')
\end{Verbatim}
            
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_9_1.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_9_2.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \section{Problem 5 - Surface Energy
Balance}\label{problem-5---surface-energy-balance}

\paragraph{The surface energy balance is typically zero meaning that the
surface is in thermal equilibrium. Surface energy balance is positive on
some days because the outgoing longwave cannot keep up with the other
fluxes, snow cannot heat up past zero degrees! On days with a positive
SEB, the excess energy goes to melt or sublimation. I'm very surprised
to see sustained positive SEB in winter at AWS 4. I think this is likely
some sort of processing or instrument error as air temperature are well
below zero durring these times. Or could a positive SEB be attributed to
sublimation of surface
snow?}\label{the-surface-energy-balance-is-typically-zero-meaning-that-the-surface-is-in-thermal-equilibrium.-surface-energy-balance-is-positive-on-some-days-because-the-outgoing-longwave-cannot-keep-up-with-the-other-fluxes-snow-cannot-heat-up-past-zero-degrees-on-days-with-a-positive-seb-the-excess-energy-goes-to-melt-or-sublimation.-im-very-surprised-to-see-sustained-positive-seb-in-winter-at-aws-4.-i-think-this-is-likely-some-sort-of-processing-or-instrument-error-as-air-temperature-are-well-below-zero-durring-these-times.-or-could-a-positive-seb-be-attributed-to-sublimation-of-surface-snow}

    \begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}6}]:} \PY{c+c1}{\PYZsh{} Caclulate SEB}
        \PY{n}{aws4\PYZus{}SEB} \PY{o}{=} \PY{n}{aws4\PYZus{}ISWR} \PY{o}{\PYZhy{}} \PY{n}{aws4\PYZus{}OSWR} \PY{o}{+} \PY{n}{aws4\PYZus{}ILWR} \PY{o}{\PYZhy{}} \PY{n}{aws4\PYZus{}OLWR} \PY{o}{+} \PY{n}{aws4\PYZus{}SHF} \PY{o}{+} \PY{n}{aws4\PYZus{}LHF} \PY{o}{+} \PY{n}{aws4\PYZus{}GHF}
        \PY{n}{aws9\PYZus{}SEB} \PY{o}{=} \PY{n}{aws9\PYZus{}ISWR} \PY{o}{\PYZhy{}} \PY{n}{aws9\PYZus{}OSWR} \PY{o}{+} \PY{n}{aws9\PYZus{}ILWR} \PY{o}{\PYZhy{}} \PY{n}{aws9\PYZus{}OLWR} \PY{o}{+} \PY{n}{aws9\PYZus{}SHF} \PY{o}{+} \PY{n}{aws9\PYZus{}LHF} \PY{o}{+} \PY{n}{aws9\PYZus{}GHF}
        
        \PY{c+c1}{\PYZsh{} Plot SEB}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}SEB}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 4}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}SEB}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 9}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Energy Balance}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{W/m\PYZca{}2}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot surface temperature}
        \PY{n}{aws9\PYZus{}ts} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{5}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mf}{273.15}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ts}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 4}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}ts}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 9}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Temperature}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Degrees C}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot air temperature at AWS 4}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}t2m}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 4 2 m Air Temperature}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Degrees C}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}6}]:} Text(0, 0.5, 'Degrees C')
\end{Verbatim}
            
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_11_1.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_11_2.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_11_3.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \section{Problem 6 - Albedo}\label{problem-6---albedo}

\paragraph{Note that I am plotting 10 day running means. For this
analysis I focus on high summer (defined as January, February, November,
and December) as this is when surface melting is most likely to occur,
also becuase albedo is poorly defined in winter (dividing by zero). AWS
9 tends to have lower surface albedo than AWS 4. I actually find this a
bit surprising given the higher solar zenith angles at AWS 9 and that
surface melt at AWS 4 is much more likely than at AWS 9. However,
perhaps more frequent fresh snowfall and therefore smaller snow grains
could explain the generally higher surface albedo at AWS 4. Notebally
AWS 4 has more albedo variability, perhaps because more frequent cycles
of surface melt and new snowfall. Interestingly, at both stations albedo
decreases moving closer to the middle of summer. I wonder if this is
because of melt or becuase lower solar zenith angles. You can see that
periods of surface melting at AWS 4 correspond to reductions in surface
albedo, whereas AWS 9 does not have surface
melting}\label{note-that-i-am-plotting-10-day-running-means.-for-this-analysis-i-focus-on-high-summer-defined-as-january-february-november-and-december-as-this-is-when-surface-melting-is-most-likely-to-occur-also-becuase-albedo-is-poorly-defined-in-winter-dividing-by-zero.-aws-9-tends-to-have-lower-surface-albedo-than-aws-4.-i-actually-find-this-a-bit-surprising-given-the-higher-solar-zenith-angles-at-aws-9-and-that-surface-melt-at-aws-4-is-much-more-likely-than-at-aws-9.-however-perhaps-more-frequent-fresh-snowfall-and-therefore-smaller-snow-grains-could-explain-the-generally-higher-surface-albedo-at-aws-4.-notebally-aws-4-has-more-albedo-variability-perhaps-because-more-frequent-cycles-of-surface-melt-and-new-snowfall.-interestingly-at-both-stations-albedo-decreases-moving-closer-to-the-middle-of-summer.-i-wonder-if-this-is-because-of-melt-or-becuase-lower-solar-zenith-angles.-you-can-see-that-periods-of-surface-melting-at-aws-4-correspond-to-reductions-in-surface-albedo-whereas-aws-9-does-not-have-surface-melting}

    \begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}7}]:} \PY{c+c1}{\PYZsh{} Load data}
        \PY{n}{aws4\PYZus{}ISWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{11}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)}
        \PY{n}{aws4\PYZus{}OSWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws4\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{12}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}ISWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{11}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        \PY{n}{aws9\PYZus{}OSWR} \PY{o}{=} \PY{n}{aws\PYZus{}timeseries}\PY{p}{(}\PY{n}{aws9\PYZus{}path}\PY{p}{,} \PY{l+m+mi}{12}\PY{p}{)}\PY{o}{.}\PY{n}{rolling}\PY{p}{(}\PY{n}{window}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)} 
        
        \PY{c+c1}{\PYZsh{} Calculate albedo}
        \PY{n}{aws4\PYZus{}albedo} \PY{o}{=} \PY{n}{aws4\PYZus{}OSWR} \PY{o}{/} \PY{n}{aws4\PYZus{}ISWR}
        \PY{n}{aws9\PYZus{}albedo} \PY{o}{=} \PY{n}{aws9\PYZus{}OSWR} \PY{o}{/} \PY{n}{aws9\PYZus{}ISWR}
        
        \PY{c+c1}{\PYZsh{} Plot}
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}albedo}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 4}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}albedo}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 9}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Albedo}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
        
        \PY{c+c1}{\PYZsh{} Plot surface temperature }
        \PY{n}{fig} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws4\PYZus{}ts}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 4}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{aws9\PYZus{}ts}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{AWS 9}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{grid}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Surface Temperature}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
        \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Degrees C}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{14}\PY{p}{)}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}7}]:} Text(0, 0.5, 'Degrees C')
\end{Verbatim}
            
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_13_1.png}
    \end{center}
    { \hspace*{\fill} \\}
    
    \begin{center}
    \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_13_2.png}
    \end{center}
    { \hspace*{\fill} \\}
    

    % Add a bibliography block to the postdoc
    
    
    
    \end{document}
